The 2013–14 FC Terek Grozny season was the sixth successive season that Terek played in the Russian Premier League, the highest tier of football in Russia.

They finished the season in 12th place and reached the Quarter-finals of the Russian Cup where they were defeated by CSKA Moscow.

Terek Grozny appointed Yuri Krasnozhan during pre-season, following the expiration of Stanislav Cherchesov contract.

On 28 October 2013 Krasnozhan resigned as manager of Terek with them 14th in the table,[1] Vait Talgayev was appointed as a caretaker manager the following day.

[2] After a week with Vait Talgayev in charge, Terek appointed Rashid Rakhimov as their permanent successor to Yuri Krasnozhan.